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arXiv · 2210.11183

$L_p\rightarrow L_q$ boundedness of Fourier multipliers

Medet Nursultanov
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Abstract

We investigate the $L_p \mapsto L_q$ boundedness of the Fourier multipliers. We obtain sufficient conditions, namely, we derive Hormander and Lizorkin type theorems. We also obtain the necessary conditions. For $M$-generalized monotone functions, we obtain a criteria for boundedness of the corresponding Fourier multipliers.

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Medet Nursultanov. 2022-10-20. $L_p\rightarrow L_q$ boundedness of Fourier multipliers. https://arxiv.org/abs/2210.11183

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